Files
ParkingRobot/ClumsyPilot/ParkrobTrajplanner/PathSmoothing/LocalG2/LocalG2CandidateBuilder.cs
T

1099 lines
52 KiB
C#

using System;
using System.Collections.Generic;
using System.Collections.ObjectModel;
using System.Threading;
using MultiWheelC.TrajectoryPlanning.CoarsePath;
using MultiWheelC.TrajectoryPlanning.PathSmoothing.Processing;
using MultiWheelC.TrajectoryPlanning.Utils;
namespace MultiWheelC.TrajectoryPlanning.PathSmoothing.LocalG2;
/// <summary>以固定窗口和尺度顺序构造有限的局部五次 Hermite G2 候选。</summary>
internal sealed class LocalG2CandidateBuilder
{
private const double MinimumDerivativeNorm = 1e-10d;
private const int MaximumDerivativeCertificationDepth = 40;
private const int MaximumDerivativeCertificationIntervals = 8192;
private const double DerivativeCertificationMargin = 1e-12d;
private const int MaximumSubdivisionDepth = 32;
private static readonly double[] DerivativeScaleMultipliers = { 1d, 0.85d, 1.15d };
internal IReadOnlyList<LocalG2CandidateGeometry> Build(
PreparedDirectionSegment originalSegment,
LocalG2SmoothingRegion region,
double outputSpacingMeters,
LocalG2OptionsSnapshot options,
CancellationToken cancellationToken)
{
if (!IsValidInput(originalSegment, region, outputSpacingMeters, options)) return Empty();
var candidates = new List<LocalG2CandidateGeometry>();
for (int windowIndex = 0; windowIndex < region.WindowVariants.Count; windowIndex++)
{
LocalG2WindowVariant window = region.WindowVariants[windowIndex];
for (int scaleIndex = 0; scaleIndex < DerivativeScaleMultipliers.Length; scaleIndex++)
{
cancellationToken.ThrowIfCancellationRequested();
if (candidates.Count >= Math.Min(options.MaximumCandidatesPerRegion, 12)) return ReadOnly(candidates);
if (TryBuildCandidate(
candidates.Count,
originalSegment,
region,
window,
DerivativeScaleMultipliers[scaleIndex],
outputSpacingMeters,
cancellationToken,
out LocalG2CandidateGeometry candidate))
{
candidates.Add(candidate);
}
}
}
return ReadOnly(candidates);
}
private static bool TryBuildCandidate(
int candidateIndex,
PreparedDirectionSegment segment,
LocalG2SmoothingRegion region,
LocalG2WindowVariant window,
double multiplier,
double outputSpacingMeters,
CancellationToken cancellationToken,
out LocalG2CandidateGeometry candidate)
{
candidate = null;
if (!PathReferenceInterpolator.TryInterpolateByArcLength(segment.Points, window.StartArcLengthMeters, out SmoothingPoint2D startReference, out _) ||
!PathReferenceInterpolator.TryInterpolateByArcLength(segment.Points, window.EndArcLengthMeters, out SmoothingPoint2D endReference, out _))
{
return false;
}
double directionSign = segment.Direction == TravelDirection.Forward ? 1d : -1d;
CurvatureTransition first = region.Transitions[0];
CurvatureTransition last = region.Transitions[region.Transitions.Count - 1];
bool firstAtStart = SameArc(first.LocalArcLengthMeters, window.StartArcLengthMeters);
bool lastAtEnd = SameArc(last.LocalArcLengthMeters, window.EndArcLengthMeters);
double startVehicleCurvature = firstAtStart && segment.StartVehicleCurvaturePerMeter.HasValue
? segment.StartVehicleCurvaturePerMeter.Value
: first.LeftVehicleCurvaturePerMeter;
double endVehicleCurvature = last.RightVehicleCurvaturePerMeter;
if (!NumericGuard.IsFinite(startVehicleCurvature) || !NumericGuard.IsFinite(endVehicleCurvature)) return false;
var nodes = new List<BoundaryNode>();
nodes.Add(new BoundaryNode(window.StartArcLengthMeters, startReference.X, startReference.Y,
startReference.Heading, startVehicleCurvature));
for (int transitionIndex = 0; transitionIndex < region.Transitions.Count; transitionIndex++)
{
CurvatureTransition transition = region.Transitions[transitionIndex];
bool atStart = SameArc(transition.LocalArcLengthMeters, window.StartArcLengthMeters);
bool atEnd = SameArc(transition.LocalArcLengthMeters, window.EndArcLengthMeters);
// A one-sided transition at a hard segment boundary has no left/right zero-length piece.
if (atStart || atEnd) continue;
double leftAvailable = transition.LocalArcLengthMeters - window.StartArcLengthMeters;
double rightAvailable = window.EndArcLengthMeters - transition.LocalArcLengthMeters;
double denominator = leftAvailable + rightAvailable;
if (!NumericGuard.IsPositiveFinite(denominator)) return false;
double sharedCurvature = transition.LeftVehicleCurvaturePerMeter +
(transition.RightVehicleCurvaturePerMeter - transition.LeftVehicleCurvaturePerMeter) * leftAvailable / denominator;
if (!NumericGuard.IsFinite(sharedCurvature)) return false;
nodes.Add(new BoundaryNode(transition.LocalArcLengthMeters, transition.X, transition.Y,
transition.VehicleHeadingRadians, sharedCurvature));
}
nodes.Add(new BoundaryNode(window.EndArcLengthMeters, endReference.X, endReference.Y,
endReference.Heading, endVehicleCurvature));
if (!TryAssignDerivativeScales(nodes, multiplier) || nodes.Count < 2) return false;
var sampled = new List<SmoothingPoint2D>();
for (int nodeIndex = 1; nodeIndex < nodes.Count; nodeIndex++)
{
cancellationToken.ThrowIfCancellationRequested();
BoundaryNode left = nodes[nodeIndex - 1];
BoundaryNode right = nodes[nodeIndex];
if (!TryCreateCurve(left, right, directionSign, out QuinticHermiteCurve2D curve)) return false;
if (!TryAppendCurveSamples(
curve,
left,
right,
segment,
outputSpacingMeters,
sampled,
cancellationToken))
{
return false;
}
}
if (sampled.Count < 2) return false;
candidate = new LocalG2CandidateGeometry(
candidateIndex,
segment.SegmentIndex,
window.StartArcLengthMeters,
window.EndArcLengthMeters,
window.LeftWindowLengthMeters,
window.RightWindowLengthMeters,
sampled,
startVehicleCurvature,
endVehicleCurvature,
directionSign * startVehicleCurvature,
directionSign * endVehicleCurvature,
true);
return true;
}
private static bool TryAssignDerivativeScales(List<BoundaryNode> nodes, double multiplier)
{
if (!NumericGuard.IsPositiveFinite(multiplier)) return false;
for (int index = 0; index < nodes.Count; index++)
{
double scale;
if (index == 0) scale = nodes[1].ArcLengthMeters - nodes[0].ArcLengthMeters;
else if (index == nodes.Count - 1) scale = nodes[index].ArcLengthMeters - nodes[index - 1].ArcLengthMeters;
else scale = ((nodes[index].ArcLengthMeters - nodes[index - 1].ArcLengthMeters) +
(nodes[index + 1].ArcLengthMeters - nodes[index].ArcLengthMeters)) / 2d;
scale *= multiplier;
if (!NumericGuard.IsPositiveFinite(scale)) return false;
nodes[index] = nodes[index].WithDerivativeScale(scale);
}
return true;
}
private static bool TryCreateCurve(BoundaryNode left, BoundaryNode right, double directionSign, out QuinticHermiteCurve2D curve)
{
curve = null;
if (!TryGetDerivatives(left, directionSign, out double ldx, out double ldy, out double lddx, out double lddy) ||
!TryGetDerivatives(right, directionSign, out double rdx, out double rdy, out double rddx, out double rddy))
{
return false;
}
return QuinticHermiteCurve2D.TryCreate(left.X, left.Y, ldx, ldy, lddx, lddy,
right.X, right.Y, rdx, rdy, rddx, rddy, out curve, out _);
}
private static bool TryGetDerivatives(BoundaryNode node, double directionSign,
out double dx, out double dy, out double ddx, out double ddy)
{
dx = dy = ddx = ddy = 0d;
double travelHeading = directionSign > 0d ? node.VehicleHeadingRadians : node.VehicleHeadingRadians - Math.PI;
double geometricCurvature = directionSign * node.VehicleCurvaturePerMeter;
double tx = Math.Cos(travelHeading);
double ty = Math.Sin(travelHeading);
double nx = -ty;
double ny = tx;
dx = node.DerivativeScale * tx;
dy = node.DerivativeScale * ty;
ddx = node.DerivativeScale * node.DerivativeScale * geometricCurvature * nx;
ddy = node.DerivativeScale * node.DerivativeScale * geometricCurvature * ny;
return NumericGuard.IsFinite(dx) && NumericGuard.IsFinite(dy) && NumericGuard.IsFinite(ddx) && NumericGuard.IsFinite(ddy) &&
Math.Sqrt(dx * dx + dy * dy) >= MinimumDerivativeNorm;
}
private static bool TryAppendCurveSamples(
QuinticHermiteCurve2D curve,
BoundaryNode left,
BoundaryNode right,
PreparedDirectionSegment segment,
double outputSpacingMeters,
List<SmoothingPoint2D> output,
CancellationToken cancellationToken)
{
// A short endpoint chord and a finite sample grid cannot rule out an interior cusp.
// Certify a derivative-norm lower bound over the whole parameter interval first.
if (!TryCertifyDerivativeLowerBound(curve)) return false;
if (!TryEvaluate(curve, 0d, out CurveSample start) || !TryEvaluate(curve, 1d, out CurveSample end)) return false;
if (output.Count == 0 && !TryAppendPoint(start, left, right, segment, output)) return false;
return TrySubdivide(curve, left, right, segment, outputSpacingMeters, 0d, start, 1d, end, 0, output, cancellationToken);
}
private static bool TrySubdivide(
QuinticHermiteCurve2D curve,
BoundaryNode left,
BoundaryNode right,
PreparedDirectionSegment segment,
double outputSpacingMeters,
double u0,
CurveSample sample0,
double u1,
CurveSample sample1,
int depth,
List<SmoothingPoint2D> output,
CancellationToken cancellationToken)
{
cancellationToken.ThrowIfCancellationRequested();
if (Distance(sample0, sample1) <= outputSpacingMeters)
{
return TryAppendPoint(sample1, left, right, segment, output);
}
if (depth >= MaximumSubdivisionDepth) return false;
double middle = (u0 + u1) / 2d;
if (!TryEvaluate(curve, middle, out CurveSample middleSample)) return false;
return TrySubdivide(curve, left, right, segment, outputSpacingMeters, u0, sample0, middle, middleSample,
depth + 1, output, cancellationToken) &&
TrySubdivide(curve, left, right, segment, outputSpacingMeters, middle, middleSample, u1, sample1,
depth + 1, output, cancellationToken);
}
private static bool TryAppendPoint(
CurveSample sample,
BoundaryNode left,
BoundaryNode right,
PreparedDirectionSegment segment,
List<SmoothingPoint2D> output)
{
double referenceArcLength = left.ArcLengthMeters + (right.ArcLengthMeters - left.ArcLengthMeters) * sample.Parameter;
if (!PathReferenceInterpolator.TryInterpolateByArcLength(segment.Points, referenceArcLength, out SmoothingPoint2D reference, out _))
return false;
double x = SameArc(sample.Parameter, 0d) ? left.X : SameArc(sample.Parameter, 1d) ? right.X : sample.X;
double y = SameArc(sample.Parameter, 0d) ? left.Y : SameArc(sample.Parameter, 1d) ? right.Y : sample.Y;
double travelHeading = Math.Atan2(sample.Dy, sample.Dx);
double vehicleHeading = segment.Direction == TravelDirection.Forward ? travelHeading : travelHeading + Math.PI;
if (!NumericGuard.IsFinite(x) || !NumericGuard.IsFinite(y) || !NumericGuard.IsFinite(travelHeading) || !NumericGuard.IsFinite(vehicleHeading)) return false;
if (output.Count > 0 && Distance(output[output.Count - 1], x, y) <= 1e-12d) return false;
output.Add(new SmoothingPoint2D(
x,
y,
referenceArcLength,
AngleMath.NormalizeRadians(vehicleHeading),
vehicleHeading,
reference.BodyClearance,
false,
SmoothedPathPointSource.LocalG2Transition));
return true;
}
private static bool TryEvaluate(QuinticHermiteCurve2D curve, double parameter, out CurveSample sample)
{
sample = default;
curve.Evaluate(parameter, out double x, out double y, out double dx, out double dy, out double ddx, out double ddy);
double derivativeNorm = Math.Sqrt(dx * dx + dy * dy);
if (!NumericGuard.IsFinite(x) || !NumericGuard.IsFinite(y) || !NumericGuard.IsFinite(dx) || !NumericGuard.IsFinite(dy) ||
!NumericGuard.IsFinite(ddx) || !NumericGuard.IsFinite(ddy) || !NumericGuard.IsFinite(derivativeNorm) ||
derivativeNorm < MinimumDerivativeNorm)
{
return false;
}
sample = new CurveSample(parameter, x, y, dx, dy);
return true;
}
private static bool TryCertifyDerivativeLowerBound(QuinticHermiteCurve2D curve)
{
if (!TryCreateDerivativeBezierControls(curve, out DerivativeControlPoint d0, out DerivativeControlPoint d1,
out DerivativeControlPoint d2, out DerivativeControlPoint d3, out DerivativeControlPoint d4))
{
return false;
}
int visitedIntervals = 0;
return TryCertifyDerivativeLowerBound(d0, d1, d2, d3, d4, 0, ref visitedIntervals);
}
private static bool TryCreateDerivativeBezierControls(
QuinticHermiteCurve2D curve,
out DerivativeControlPoint d0,
out DerivativeControlPoint d1,
out DerivativeControlPoint d2,
out DerivativeControlPoint d3,
out DerivativeControlPoint d4)
{
d0 = d1 = d2 = d3 = d4 = default;
curve.Evaluate(0d, out _, out _, out double dx0, out double dy0, out double ddx0, out double ddy0);
curve.Evaluate(0.5d, out _, out _, out double dxMiddle, out double dyMiddle, out _, out _);
curve.Evaluate(1d, out _, out _, out double dxEnd, out double dyEnd, out double ddxEnd, out double ddyEnd);
d0 = new DerivativeControlPoint(dx0, dy0);
d1 = new DerivativeControlPoint(dx0 + ddx0 / 4d, dy0 + ddy0 / 4d);
d4 = new DerivativeControlPoint(dxEnd, dyEnd);
d3 = new DerivativeControlPoint(dxEnd - ddxEnd / 4d, dyEnd - ddyEnd / 4d);
d2 = new DerivativeControlPoint(
(16d * dxMiddle - d0.X - 4d * d1.X - 4d * d3.X - d4.X) / 6d,
(16d * dyMiddle - d0.Y - 4d * d1.Y - 4d * d3.Y - d4.Y) / 6d);
return d0.IsFinite && d1.IsFinite && d2.IsFinite && d3.IsFinite && d4.IsFinite;
}
private static bool TryCertifyDerivativeLowerBound(
DerivativeControlPoint d0,
DerivativeControlPoint d1,
DerivativeControlPoint d2,
DerivativeControlPoint d3,
DerivativeControlPoint d4,
int depth,
ref int visitedIntervals)
{
if (++visitedIntervals > MaximumDerivativeCertificationIntervals) return false;
if (!TryGetOriginToConvexHullDistance(d0, d1, d2, d3, d4, out double lowerBound, out double margin))
return false;
if (lowerBound > MinimumDerivativeNorm + margin) return true;
if (depth >= MaximumDerivativeCertificationDepth) return false;
DerivativeControlPoint d01 = Midpoint(d0, d1);
DerivativeControlPoint d12 = Midpoint(d1, d2);
DerivativeControlPoint d23 = Midpoint(d2, d3);
DerivativeControlPoint d34 = Midpoint(d3, d4);
DerivativeControlPoint d012 = Midpoint(d01, d12);
DerivativeControlPoint d123 = Midpoint(d12, d23);
DerivativeControlPoint d234 = Midpoint(d23, d34);
DerivativeControlPoint d0123 = Midpoint(d012, d123);
DerivativeControlPoint d1234 = Midpoint(d123, d234);
DerivativeControlPoint middle = Midpoint(d0123, d1234);
if (!d01.IsFinite || !d12.IsFinite || !d23.IsFinite || !d34.IsFinite || !d012.IsFinite || !d123.IsFinite ||
!d234.IsFinite || !d0123.IsFinite || !d1234.IsFinite || !middle.IsFinite)
{
return false;
}
return TryCertifyDerivativeLowerBound(d0, d01, d012, d0123, middle, depth + 1, ref visitedIntervals) &&
TryCertifyDerivativeLowerBound(middle, d1234, d234, d34, d4, depth + 1, ref visitedIntervals);
}
private static bool TryGetOriginToConvexHullDistance(
DerivativeControlPoint d0,
DerivativeControlPoint d1,
DerivativeControlPoint d2,
DerivativeControlPoint d3,
DerivativeControlPoint d4,
out double distance,
out double margin)
{
distance = 0d;
margin = 0d;
var controls = new[] { d0, d1, d2, d3, d4 };
double maximumCoordinate = 0d;
for (int index = 0; index < controls.Length; index++)
{
if (!controls[index].IsFinite) return false;
maximumCoordinate = Math.Max(maximumCoordinate, Math.Max(Math.Abs(controls[index].X), Math.Abs(controls[index].Y)));
}
if (!NumericGuard.IsFinite(maximumCoordinate)) return false;
margin = DerivativeCertificationMargin * Math.Max(1d, maximumCoordinate);
for (int first = 0; first < controls.Length - 2; first++)
{
for (int second = first + 1; second < controls.Length - 1; second++)
{
for (int third = second + 1; third < controls.Length; third++)
{
if (ContainsOrigin(controls[first], controls[second], controls[third], margin)) return true;
}
}
}
distance = double.PositiveInfinity;
for (int first = 0; first < controls.Length; first++)
{
distance = Math.Min(distance, controls[first].Norm);
for (int second = first + 1; second < controls.Length; second++)
distance = Math.Min(distance, DistanceToSegment(controls[first], controls[second]));
}
return NumericGuard.IsFinite(distance);
}
private static bool ContainsOrigin(DerivativeControlPoint first, DerivativeControlPoint second,
DerivativeControlPoint third, double margin)
{
double sideX = second.X - first.X;
double sideY = second.Y - first.Y;
double thirdOffsetX = third.X - first.X;
double thirdOffsetY = third.Y - first.Y;
double triangleArea = sideX * thirdOffsetY - sideY * thirdOffsetX;
double crossFirstSecond = Cross(first, second);
double crossSecondThird = Cross(second, third);
double crossThirdFirst = Cross(third, first);
if (!NumericGuard.IsFinite(triangleArea) || !NumericGuard.IsFinite(crossFirstSecond) ||
!NumericGuard.IsFinite(crossSecondThird) || !NumericGuard.IsFinite(crossThirdFirst))
{
return true;
}
double areaMargin = margin * Math.Max(1d, Math.Max(first.Norm, Math.Max(second.Norm, third.Norm)));
if (!NumericGuard.IsFinite(areaMargin)) return true;
if (Math.Abs(triangleArea) <= areaMargin)
{
// A degenerate triangle is only a closed line segment (or a point), not a
// two-dimensional region. Treat it as origin-containing only when the origin
// lies on one of its actual closed segments; otherwise its distance is positive.
return IsOriginOnSegment(first, second, margin) || IsOriginOnSegment(second, third, margin) ||
IsOriginOnSegment(third, first, margin);
}
return (crossFirstSecond >= -areaMargin && crossSecondThird >= -areaMargin && crossThirdFirst >= -areaMargin) ||
(crossFirstSecond <= areaMargin && crossSecondThird <= areaMargin && crossThirdFirst <= areaMargin);
}
private static bool IsOriginOnSegment(DerivativeControlPoint start, DerivativeControlPoint end, double margin)
{
double dx = end.X - start.X;
double dy = end.Y - start.Y;
double lengthSquared = dx * dx + dy * dy;
if (!NumericGuard.IsFinite(lengthSquared)) return true;
if (lengthSquared == 0d) return start.Norm <= margin;
double length = Math.Sqrt(lengthSquared);
double cross = Cross(start, end);
double projection = -(start.X * dx + start.Y * dy);
if (!NumericGuard.IsFinite(length) || !NumericGuard.IsFinite(cross) || !NumericGuard.IsFinite(projection)) return true;
double lineMargin = margin * Math.Max(1d, length);
double projectionMargin = margin * Math.Max(1d, length);
if (!NumericGuard.IsFinite(lineMargin) || !NumericGuard.IsFinite(projectionMargin)) return true;
return Math.Abs(cross) <= lineMargin && projection >= -projectionMargin &&
projection <= lengthSquared + projectionMargin;
}
private static double DistanceToSegment(DerivativeControlPoint start, DerivativeControlPoint end)
{
double dx = end.X - start.X;
double dy = end.Y - start.Y;
double denominator = dx * dx + dy * dy;
if (!NumericGuard.IsFinite(denominator)) return double.NaN;
if (denominator == 0d) return start.Norm;
double parameter = -(start.X * dx + start.Y * dy) / denominator;
if (!NumericGuard.IsFinite(parameter)) return double.NaN;
parameter = Math.Max(0d, Math.Min(1d, parameter));
double x = start.X + parameter * dx;
double y = start.Y + parameter * dy;
return Math.Sqrt(x * x + y * y);
}
private static DerivativeControlPoint Midpoint(DerivativeControlPoint left, DerivativeControlPoint right) =>
new DerivativeControlPoint((left.X + right.X) / 2d, (left.Y + right.Y) / 2d);
private static double Cross(DerivativeControlPoint left, DerivativeControlPoint right) => left.X * right.Y - left.Y * right.X;
private static bool IsValidInput(PreparedDirectionSegment segment, LocalG2SmoothingRegion region,
double outputSpacingMeters, LocalG2OptionsSnapshot options)
{
if (segment == null || region == null || options == null || segment.SegmentIndex != region.SegmentIndex ||
!NumericGuard.IsPositiveFinite(outputSpacingMeters) || segment.Points == null || segment.Points.Count < 2 ||
region.Transitions == null || region.Transitions.Count == 0 || region.WindowVariants == null)
{
return false;
}
for (int index = 0; index < region.Transitions.Count; index++)
{
CurvatureTransition transition = region.Transitions[index];
if (transition == null || transition.SegmentIndex != segment.SegmentIndex) return false;
}
return true;
}
private static double Distance(CurveSample left, CurveSample right) => Distance(left.X, left.Y, right.X, right.Y);
private static double Distance(SmoothingPoint2D point, double x, double y) => Distance(point.X, point.Y, x, y);
private static double Distance(double x0, double y0, double x1, double y1)
{
double dx = x1 - x0;
double dy = y1 - y0;
return Math.Sqrt(dx * dx + dy * dy);
}
private static bool SameArc(double left, double right) => Math.Abs(left - right) <= 1e-10d;
private static IReadOnlyList<LocalG2CandidateGeometry> Empty() => new ReadOnlyCollection<LocalG2CandidateGeometry>(new List<LocalG2CandidateGeometry>());
private static IReadOnlyList<LocalG2CandidateGeometry> ReadOnly(List<LocalG2CandidateGeometry> values) =>
new ReadOnlyCollection<LocalG2CandidateGeometry>(values);
private readonly struct BoundaryNode
{
internal BoundaryNode(double arcLengthMeters, double x, double y, double vehicleHeadingRadians, double vehicleCurvaturePerMeter)
{
ArcLengthMeters = arcLengthMeters;
X = x;
Y = y;
VehicleHeadingRadians = vehicleHeadingRadians;
VehicleCurvaturePerMeter = vehicleCurvaturePerMeter;
DerivativeScale = 0d;
}
private BoundaryNode(double arcLengthMeters, double x, double y, double vehicleHeadingRadians,
double vehicleCurvaturePerMeter, double derivativeScale)
{
ArcLengthMeters = arcLengthMeters;
X = x;
Y = y;
VehicleHeadingRadians = vehicleHeadingRadians;
VehicleCurvaturePerMeter = vehicleCurvaturePerMeter;
DerivativeScale = derivativeScale;
}
internal double ArcLengthMeters { get; }
internal double X { get; }
internal double Y { get; }
internal double VehicleHeadingRadians { get; }
internal double VehicleCurvaturePerMeter { get; }
internal double DerivativeScale { get; }
internal BoundaryNode WithDerivativeScale(double derivativeScale) => new BoundaryNode(
ArcLengthMeters, X, Y, VehicleHeadingRadians, VehicleCurvaturePerMeter, derivativeScale);
}
private readonly struct CurveSample
{
internal CurveSample(double parameter, double x, double y, double dx, double dy)
{
Parameter = parameter;
X = x;
Y = y;
Dx = dx;
Dy = dy;
}
internal double Parameter { get; }
internal double X { get; }
internal double Y { get; }
internal double Dx { get; }
internal double Dy { get; }
}
private readonly struct DerivativeControlPoint
{
internal DerivativeControlPoint(double x, double y)
{
X = x;
Y = y;
}
internal double X { get; }
internal double Y { get; }
internal bool IsFinite => NumericGuard.IsFinite(X) && NumericGuard.IsFinite(Y);
internal double Norm => Math.Sqrt(X * X + Y * Y);
}
/// <summary>反射脚本使用的窄范围候选与拼接场景入口。</summary>
public static class TestHooks
{
public static CandidateTestSnapshot Execute(string scenario)
{
if (string.IsNullOrWhiteSpace(scenario)) throw new ArgumentException("A scenario is required.", nameof(scenario));
switch (scenario)
{
case "Isolated": return BuildIsolated();
case "Cluster": return BuildCluster();
case "Reverse": return BuildReverse();
case "Spliced": return BuildSpliced();
case "StartBoundary": return BuildStartBoundary();
case "InteriorStationaryCurve": return BuildInteriorStationaryCurve();
case "ConstantVelocityCurve": return BuildConstantVelocityCurve();
case "ExactSpliceEndpoints": return BuildExactSpliceEndpoints();
case "GearBoundary": return BuildGearBoundary();
case "TwoRegionWorkOrder": return BuildTwoRegionWorkOrder();
default: throw new ArgumentOutOfRangeException(nameof(scenario));
}
}
public sealed class CandidateTestSnapshot
{
internal CandidateTestSnapshot(int candidateCount, double startPositionError, double endPositionError,
double startCurvatureError, double endCurvatureError, bool containsLocalG2Source,
int outputRegionCount, bool internalConnectionsAreG2, string direction,
bool vehicleAndGeometricCurvatureSignsAreOpposite, bool noDuplicateNonGearPoints,
bool endpointsUnchanged, bool rejected = false, bool endpointsAreExact = false,
bool gearBoundaryMarkerPreserved = false, bool accepted = false,
bool workOrderDescending = false, bool frontArcPreservedAfterBackReplacement = false,
bool bothReplacementsRetained = false, bool forwardOrderRejected = false,
bool deterministicWorkOrder = false, bool invalidWorkOrderRejected = false)
{
CandidateCount = candidateCount;
StartPositionError = startPositionError;
EndPositionError = endPositionError;
StartCurvatureError = startCurvatureError;
EndCurvatureError = endCurvatureError;
ContainsLocalG2Source = containsLocalG2Source;
OutputRegionCount = outputRegionCount;
InternalConnectionsAreG2 = internalConnectionsAreG2;
Direction = direction;
VehicleAndGeometricCurvatureSignsAreOpposite = vehicleAndGeometricCurvatureSignsAreOpposite;
NoDuplicateNonGearPoints = noDuplicateNonGearPoints;
EndpointsUnchanged = endpointsUnchanged;
Rejected = rejected;
EndpointsAreExact = endpointsAreExact;
GearBoundaryMarkerPreserved = gearBoundaryMarkerPreserved;
Accepted = accepted;
WorkOrderDescending = workOrderDescending;
FrontArcPreservedAfterBackReplacement = frontArcPreservedAfterBackReplacement;
BothReplacementsRetained = bothReplacementsRetained;
ForwardOrderRejected = forwardOrderRejected;
DeterministicWorkOrder = deterministicWorkOrder;
InvalidWorkOrderRejected = invalidWorkOrderRejected;
}
public int CandidateCount { get; }
public double StartPositionError { get; }
public double EndPositionError { get; }
public double StartCurvatureError { get; }
public double EndCurvatureError { get; }
public bool ContainsLocalG2Source { get; }
public int OutputRegionCount { get; }
public bool InternalConnectionsAreG2 { get; }
public string Direction { get; }
public bool VehicleAndGeometricCurvatureSignsAreOpposite { get; }
public bool NoDuplicateNonGearPoints { get; }
public bool EndpointsUnchanged { get; }
public bool Rejected { get; }
public bool EndpointsAreExact { get; }
public bool GearBoundaryMarkerPreserved { get; }
public bool Accepted { get; }
public bool WorkOrderDescending { get; }
public bool FrontArcPreservedAfterBackReplacement { get; }
public bool BothReplacementsRetained { get; }
public bool ForwardOrderRejected { get; }
public bool DeterministicWorkOrder { get; }
public bool InvalidWorkOrderRejected { get; }
}
private static CandidateTestSnapshot BuildIsolated()
{
PreparedDirectionSegment segment = CreateSegment(TravelDirection.Forward, null);
LocalG2SmoothingRegion region = CreateRegion(new[]
{
new CurvatureTransition(0, 1, 2, 0.5d, 0.5d, 0d, 0d, 0d, 0.4d),
}, 0.25d, 0.75d);
IReadOnlyList<LocalG2CandidateGeometry> candidates = new LocalG2CandidateBuilder().Build(
segment, region, 0.025d, CreateOptions(), CancellationToken.None);
if (candidates.Count == 0) throw new InvalidOperationException("The isolated candidate scenario produced no candidate.");
LocalG2CandidateGeometry candidate = candidates[0];
PathReferenceInterpolator.TryInterpolateByArcLength(segment.Points, 0.25d, out SmoothingPoint2D start, out _);
PathReferenceInterpolator.TryInterpolateByArcLength(segment.Points, 0.75d, out SmoothingPoint2D end, out _);
return new CandidateTestSnapshot(candidates.Count,
Distance(start, candidate.RegionPoints[0]), Distance(end, candidate.RegionPoints[candidate.RegionPoints.Count - 1]),
Math.Abs(candidate.StartVehicleCurvaturePerMeter - 0d),
Math.Abs(candidate.EndVehicleCurvaturePerMeter - 0.4d),
ContainsLocalG2(candidate.RegionPoints), 0, false, string.Empty, false, false, false);
}
private static CandidateTestSnapshot BuildCluster()
{
PreparedDirectionSegment segment = CreateSegment(TravelDirection.Forward, null);
var transitions = new[]
{
new CurvatureTransition(0, 1, 2, 0.4d, 0.4d, 0d, 0d, 0d, 0.4d),
new CurvatureTransition(0, 2, 3, 0.6d, 0.6d, 0d, 0d, 0.4d, 0d),
};
var planner = new LocalG2WindowPlanner();
if (!planner.TryPlan(new PreparedPath(new[] { segment }), transitions, CreateOptions(),
out IReadOnlyList<LocalG2SmoothingRegion> regions, out string reason))
{
throw new InvalidOperationException(reason);
}
IReadOnlyList<LocalG2CandidateGeometry> candidates = new LocalG2CandidateBuilder().Build(
segment, regions[0], 0.025d, CreateOptions(), CancellationToken.None);
if (candidates.Count == 0) throw new InvalidOperationException("The clustered candidate scenario produced no candidate.");
return new CandidateTestSnapshot(0, 0d, 0d, 0d, 0d, false, regions.Count,
candidates[0].InternalConnectionsAreG2, string.Empty, false, false, false);
}
private static CandidateTestSnapshot BuildReverse()
{
PreparedDirectionSegment segment = CreateSegment(TravelDirection.Reverse, null);
LocalG2SmoothingRegion region = CreateRegion(new[]
{
new CurvatureTransition(0, 1, 2, 0.5d, 0.5d, 0d, Math.PI, 0.2d, 0.4d),
}, 0.25d, 0.75d);
IReadOnlyList<LocalG2CandidateGeometry> candidates = new LocalG2CandidateBuilder().Build(
segment, region, 0.025d, CreateOptions(), CancellationToken.None);
if (candidates.Count == 0) throw new InvalidOperationException("The reverse candidate scenario produced no candidate.");
LocalG2CandidateGeometry candidate = candidates[0];
bool opposite = candidate.StartVehicleCurvaturePerMeter * candidate.StartGeometricCurvaturePerMeter < 0d &&
candidate.EndVehicleCurvaturePerMeter * candidate.EndGeometricCurvaturePerMeter < 0d;
return new CandidateTestSnapshot(0, 0d, 0d, 0d, 0d, false, 0, false,
segment.Direction.ToString(), opposite, false, false);
}
private static CandidateTestSnapshot BuildSpliced()
{
PreparedDirectionSegment segment = CreateSegment(TravelDirection.Forward, 0.17d);
LocalG2SmoothingRegion region = CreateRegion(new[]
{
new CurvatureTransition(0, 1, 2, 0.5d, 0.5d, 0d, 0d, 0.17d, 0.4d),
}, 0.25d, 0.75d);
IReadOnlyList<LocalG2CandidateGeometry> candidates = new LocalG2CandidateBuilder().Build(
segment, region, 0.025d, CreateOptions(), CancellationToken.None);
if (candidates.Count == 0) throw new InvalidOperationException("The splice candidate scenario produced no candidate.");
PreparedDirectionSegment untouched = CreateSegment(TravelDirection.Reverse, null);
var path = new PreparedPath(new[] { segment, untouched });
if (!new LocalG2PathSplicer().TryReplace(path, candidates[0], out PreparedPath replaced, out string reason))
throw new InvalidOperationException(reason);
PreparedDirectionSegment result = replaced.Segments[0];
bool noDuplicates = true;
for (int index = 1; index < result.Points.Count; index++)
{
if (!result.Points[index - 1].IsGearSwitchPoint && !result.Points[index].IsGearSwitchPoint &&
Distance(result.Points[index - 1], result.Points[index]) <= 1e-12d)
{
noDuplicates = false;
break;
}
}
bool monotonicallyIncreasing = true;
for (int index = 1; index < result.Points.Count; index++)
{
if (result.Points[index].ArcLength <= result.Points[index - 1].ArcLength)
{
monotonicallyIncreasing = false;
break;
}
}
bool endpoints = Distance(segment.Points[0], result.Points[0]) <= 1e-12d &&
Distance(segment.Points[segment.Points.Count - 1], result.Points[result.Points.Count - 1]) <= 1e-12d &&
result.StartVehicleCurvaturePerMeter == segment.StartVehicleCurvaturePerMeter && monotonicallyIncreasing &&
ReferenceEquals(untouched, replaced.Segments[1]);
return new CandidateTestSnapshot(0, 0d, 0d, 0d, 0d, false, 0, false, string.Empty,
false, noDuplicates, endpoints);
}
private static CandidateTestSnapshot BuildStartBoundary()
{
PreparedDirectionSegment segment = CreateSegment(TravelDirection.Forward, 0.17d);
LocalG2SmoothingRegion region = CreateRegion(new[]
{
new CurvatureTransition(0, 0, 1, 0d, 0d, 0d, 0d, 0.17d, 0.4d),
}, 0d, 0.5d);
IReadOnlyList<LocalG2CandidateGeometry> candidates = new LocalG2CandidateBuilder().Build(
segment, region, 0.025d, CreateOptions(), CancellationToken.None);
if (candidates.Count == 0) throw new InvalidOperationException("The start-boundary transition must not create a zero-length left curve.");
LocalG2CandidateGeometry candidate = candidates[0];
return new CandidateTestSnapshot(candidates.Count,
Math.Abs(candidate.StartVehicleCurvaturePerMeter - 0.17d), 0d,
Math.Abs(candidate.StartVehicleCurvaturePerMeter - 0.17d), 0d,
ContainsLocalG2(candidate.RegionPoints), 0, false, string.Empty, false, false, false);
}
private static CandidateTestSnapshot BuildInteriorStationaryCurve()
{
const double endpointX = 0.00325d;
if (!QuinticHermiteCurve2D.TryCreate(0d, 0d, 0.01d, 0d, 0d, 0d,
endpointX, 0d, 0.01d, 0d, 0d, 0d, out QuinticHermiteCurve2D curve, out string reason))
{
throw new InvalidOperationException(reason);
}
var points = new[]
{
new SmoothingPoint2D(0d, 0d, 0d, 0d, 0d, 1d, false, SmoothedPathPointSource.Anchor),
new SmoothingPoint2D(endpointX, 0d, endpointX, 0d, 0d, 1d, false, SmoothedPathPointSource.Anchor),
};
var segment = new PreparedDirectionSegment(0, TravelDirection.Forward, points, false, false);
var sampled = new List<SmoothingPoint2D>();
bool accepted = TryAppendCurveSamples(curve,
new BoundaryNode(0d, 0d, 0d, 0d, 0d),
new BoundaryNode(endpointX, endpointX, 0d, 0d, 0d),
segment, 0.025d, sampled, CancellationToken.None);
return new CandidateTestSnapshot(0, 0d, 0d, 0d, 0d, false, 0, false, string.Empty,
false, false, false, !accepted);
}
private static CandidateTestSnapshot BuildConstantVelocityCurve()
{
if (!QuinticHermiteCurve2D.TryCreate(0d, 0d, 1d, 0d, 0d, 0d,
1d, 0d, 1d, 0d, 0d, 0d, out QuinticHermiteCurve2D curve, out string reason))
{
throw new InvalidOperationException(reason);
}
var points = new[]
{
new SmoothingPoint2D(0d, 0d, 0d, 0d, 0d, 1d, false, SmoothedPathPointSource.Anchor),
new SmoothingPoint2D(1d, 0d, 1d, 0d, 0d, 1d, false, SmoothedPathPointSource.Anchor),
};
var segment = new PreparedDirectionSegment(0, TravelDirection.Forward, points, false, false);
var sampled = new List<SmoothingPoint2D>();
bool accepted = TryAppendCurveSamples(curve,
new BoundaryNode(0d, 0d, 0d, 0d, 0d),
new BoundaryNode(1d, 1d, 0d, 0d, 0d),
segment, 0.025d, sampled, CancellationToken.None);
return new CandidateTestSnapshot(0, 0d, 0d, 0d, 0d, false, 0, false, string.Empty,
false, false, false, false, false, false, accepted);
}
private static CandidateTestSnapshot BuildExactSpliceEndpoints()
{
PreparedDirectionSegment segment = CreateSegment(TravelDirection.Forward, null);
var candidate = new LocalG2CandidateGeometry(0, 0, 0.25d, 0.75d, 0.25d, 0.25d,
new[]
{
Point(0.2500000005d, 0d, 0.25d, false),
Point(0.5d, 0d, 0.5d, false),
Point(0.7499999995d, 0d, 0.75d, false),
}, 0d, 0d, 0d, 0d, true);
if (!new LocalG2PathSplicer().TryReplace(new PreparedPath(new[] { segment }), candidate,
out PreparedPath replaced, out string reason))
{
throw new InvalidOperationException(reason);
}
PathReferenceInterpolator.TryInterpolateByArcLength(segment.Points, 0.25d, out SmoothingPoint2D start, out _);
PathReferenceInterpolator.TryInterpolateByArcLength(segment.Points, 0.75d, out SmoothingPoint2D end, out _);
IReadOnlyList<SmoothingPoint2D> result = replaced.Segments[0].Points;
bool exact = result[1].X == start.X && result[1].Y == start.Y &&
result[result.Count - 2].X == end.X && result[result.Count - 2].Y == end.Y;
return new CandidateTestSnapshot(0, 0d, 0d, 0d, 0d, false, 0, false, string.Empty,
false, false, false, false, exact);
}
private static CandidateTestSnapshot BuildGearBoundary()
{
var sourcePoints = new[]
{
Point(0d, 0d, 0d, true), Point(0.25d, 0d, 0.25d, false), Point(0.5d, 0d, 0.5d, false),
};
var segment = new PreparedDirectionSegment(0, TravelDirection.Forward, sourcePoints, true, false);
var candidate = new LocalG2CandidateGeometry(0, 0, 0d, 0.5d, 0d, 0.5d,
new[] { Point(0d, 0d, 0d, false), Point(0.25d, 0d, 0.25d, false), Point(0.5d, 0d, 0.5d, false) },
0d, 0d, 0d, 0d, true);
if (!new LocalG2PathSplicer().TryReplace(new PreparedPath(new[] { segment }), candidate,
out PreparedPath replaced, out string reason))
{
throw new InvalidOperationException(reason);
}
bool preserved = replaced.Segments[0].StartsAtGearSwitch && replaced.Segments[0].Points[0].IsGearSwitchPoint;
return new CandidateTestSnapshot(0, 0d, 0d, 0d, 0d, false, 0, false, string.Empty,
false, false, false, false, false, preserved);
}
private static CandidateTestSnapshot BuildTwoRegionWorkOrder()
{
var points = new List<SmoothingPoint2D>();
for (int index = 0; index <= 12; index++)
{
double arc = index * 0.25d;
points.Add(new SmoothingPoint2D(
arc,
0d,
arc,
0d,
0d,
1d,
false,
SmoothedPathPointSource.Anchor));
}
var segment = new PreparedDirectionSegment(
0,
TravelDirection.Forward,
points,
false,
false);
var original = new PreparedPath(new[] { segment });
LocalG2SmoothingRegion frontRegion = CreateOrderedRegion(0.75d, 0.5d, 1.0d, 0);
LocalG2SmoothingRegion backRegion = CreateOrderedRegion(2.25d, 2.0d, 2.5d, 1);
var reportOrder = new[] { frontRegion, backRegion };
var orderer = new LocalG2RegionWorkOrder();
if (!orderer.TryCreate(
reportOrder,
out IReadOnlyList<LocalG2SmoothingRegion> workOrder,
out string orderReason))
{
throw new InvalidOperationException(orderReason);
}
if (!orderer.TryCreate(
reportOrder,
out IReadOnlyList<LocalG2SmoothingRegion> repeatedOrder,
out string repeatedReason))
{
throw new InvalidOperationException(repeatedReason);
}
bool descending =
ReferenceEquals(backRegion, workOrder[0]) &&
ReferenceEquals(frontRegion, workOrder[1]);
bool deterministic =
ReferenceEquals(workOrder[0], repeatedOrder[0]) &&
ReferenceEquals(workOrder[1], repeatedOrder[1]) &&
ReferenceEquals(frontRegion, reportOrder[0]) &&
ReferenceEquals(backRegion, reportOrder[1]);
var wrongSegmentTransition = new CurvatureTransition(
1,
0,
1,
0.75d,
0.75d,
0d,
0d,
0d,
0.4d);
var invalidRegion = new LocalG2SmoothingRegion(
0,
new[] { wrongSegmentTransition },
0.5d,
1.0d,
new[]
{
new LocalG2WindowVariant(0, 0.5d, 1.0d, 0.25d, 0.25d),
});
bool invalidWorkOrderRejected =
!orderer.TryCreate(
new[] { invalidRegion },
out _,
out _) &&
!orderer.TryCreate(
new LocalG2SmoothingRegion[] { null },
out _,
out _);
LocalG2CandidateGeometry frontCandidate =
CreateLengthChangingCandidate(0, 0.5d, 1.0d);
LocalG2CandidateGeometry backCandidate =
CreateLengthChangingCandidate(1, 2.0d, 2.5d);
var splicer = new LocalG2PathSplicer();
if (!splicer.TryReplace(
original,
backCandidate,
out PreparedPath afterBack,
out string backReason))
{
throw new InvalidOperationException(backReason);
}
bool frontArcPreserved =
PathReferenceInterpolator.TryInterpolateByArcLength(
afterBack.Segments[0].Points,
0.5d,
out SmoothingPoint2D frontStart,
out _) &&
PathReferenceInterpolator.TryInterpolateByArcLength(
afterBack.Segments[0].Points,
1.0d,
out SmoothingPoint2D frontEnd,
out _) &&
Math.Abs(frontStart.X - 0.5d) <= 1e-12d &&
Math.Abs(frontEnd.X - 1.0d) <= 1e-12d;
if (!splicer.TryReplace(
afterBack,
frontCandidate,
out PreparedPath afterBoth,
out string frontReason))
{
throw new InvalidOperationException(frontReason);
}
int localG2PointCount = 0;
for (int index = 0; index < afterBoth.Segments[0].Points.Count; index++)
{
if (afterBoth.Segments[0].Points[index].Source ==
SmoothedPathPointSource.LocalG2Transition)
{
localG2PointCount++;
}
}
if (!splicer.TryReplace(
original,
frontCandidate,
out PreparedPath afterFront,
out string firstReason))
{
throw new InvalidOperationException(firstReason);
}
bool forwardOrderRejected = !splicer.TryReplace(
afterFront,
backCandidate,
out _,
out _);
return new CandidateTestSnapshot(
0,
0d,
0d,
0d,
0d,
false,
0,
false,
string.Empty,
false,
false,
false,
false,
false,
false,
false,
descending,
frontArcPreserved,
localG2PointCount >= 2,
forwardOrderRejected,
deterministic,
invalidWorkOrderRejected);
}
private static LocalG2SmoothingRegion CreateOrderedRegion(
double eventArc,
double startArc,
double endArc,
int index)
{
var transition = new CurvatureTransition(
0,
index,
index + 1,
eventArc,
eventArc,
0d,
0d,
0d,
0.4d);
return new LocalG2SmoothingRegion(
0,
new[] { transition },
startArc,
endArc,
new[]
{
new LocalG2WindowVariant(
0,
startArc,
endArc,
eventArc - startArc,
endArc - eventArc),
});
}
private static LocalG2CandidateGeometry CreateLengthChangingCandidate(
int candidateIndex,
double startArc,
double endArc)
{
double middleArc = 0.5d * (startArc + endArc);
var points = new[]
{
Point(startArc, 0d, startArc, false),
Point(middleArc, 0.20d, middleArc, false),
Point(endArc, 0d, endArc, false),
};
return new LocalG2CandidateGeometry(
candidateIndex,
0,
startArc,
endArc,
middleArc - startArc,
endArc - middleArc,
points,
0d,
0d,
0d,
0d,
true);
}
private static PreparedDirectionSegment CreateSegment(TravelDirection direction, double? startCurvature)
{
double heading = direction == TravelDirection.Forward ? 0d : Math.PI;
var points = new List<SmoothingPoint2D>();
for (int index = 0; index <= 4; index++)
{
double arc = index * 0.25d;
points.Add(new SmoothingPoint2D(arc, 0d, arc, heading, heading, 1d, false, SmoothedPathPointSource.Anchor));
}
return new PreparedDirectionSegment(0, direction, points, false, false, startCurvature);
}
private static LocalG2SmoothingRegion CreateRegion(
IReadOnlyList<CurvatureTransition> transitions,
double startArcLengthMeters,
double endArcLengthMeters)
{
return new LocalG2SmoothingRegion(0, transitions, startArcLengthMeters, endArcLengthMeters,
new[] { new LocalG2WindowVariant(0, startArcLengthMeters, endArcLengthMeters,
transitions[0].LocalArcLengthMeters - startArcLengthMeters,
endArcLengthMeters - transitions[transitions.Count - 1].LocalArcLengthMeters) });
}
private static LocalG2OptionsSnapshot CreateOptions() => new LocalG2OptionsSnapshot(new PathSmoothingConfiguration());
private static bool ContainsLocalG2(IReadOnlyList<SmoothingPoint2D> points)
{
for (int index = 0; index < points.Count; index++)
if (points[index].Source == SmoothedPathPointSource.LocalG2Transition) return true;
return false;
}
private static double Distance(SmoothingPoint2D left, SmoothingPoint2D right) =>
Math.Sqrt((right.X - left.X) * (right.X - left.X) + (right.Y - left.Y) * (right.Y - left.Y));
private static SmoothingPoint2D Point(double x, double y, double arcLength, bool isGearSwitch) =>
new SmoothingPoint2D(x, y, arcLength, 0d, 0d, 1d, isGearSwitch,
isGearSwitch ? SmoothedPathPointSource.GearSwitch : SmoothedPathPointSource.LocalG2Transition);
}
}